On the Borderline of Fields and Hyperfields

The hyperfield came into being due to a mathematical necessity that appeared during the study of valuation theory fields by M. Krasner, who also defined hyperring, which is related in same way as ring field. and hyperfields, well rings hyperrings, border on each other, it natural problems open questions arise their boundary areas. This paper presents such occasions, more specifically, introduces new class non-finite hyperfields hyperrings not isomorphic existing ones; classifies finite quotient or non-quotient gives answers question was raised from hyperfields: when can subtraction field F’s multiplicative subgroup G itself generate F? Furthermore, construction with regard problem isomorphism its members raises theory: give all elements F, except ones G?